If the mods are compatible with each other, then you just download and install them the way you do any mod. Go to the Mods menu, open the Mod Browser, find the mods, click Install. (This assumes that the mods in question are available in the Mod Browser in the first place. Many mods aren't; for those mods, like my own, you download the files and place them in your user directory by hand.)
If the mods aren't compatible with each other, then you'll run into problems as you play. These problems might not manifest themselves right away, and might not cause obvious problems at all. But don't assume that just because it doesn't crash right away that the mods are actually working together correctly.
No, you can't easily tell whether mods are compatible with each other without going into its source code.
No, you can't just assume that because they modify different things that they'll be compatible.
And no, you can't easily tell whether the mods are even compatible with the base game, since many of the things on the mod browser are horribly out-of-date. (You CAN find the mods' threads on this site to see if any updates have been made since the last patch date.)